Solvability of the inhomogeneous Cauchy–Riemann equation in projective weighted spaces

Polyakova, D. A.

doi:10.1134/s0037446617010189

Sib Math J

2017

DOI: 10.1134/s0037446617010189

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Solvability of the inhomogeneous Cauchy–Riemann equation in projective weighted spaces

D. A. Polyakova

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Parameter dependence of solutions of the Cauchy–Riemann equation on weighted spaces of smooth functions

Kruse

2020

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Let Ω be an open subset of R 2 and E a complete complex locally convex Hausdorff space. The purpose of this paper is to find conditions on certain weighted Fréchet spaces EV(Ω) of smooth functions and on the space E to ensure that the vector-valued Cauchy-Riemann operator ∂ : EV(Ω, E) → EV(Ω, E) is surjective. This is done via splitting theory and positive results can be interpreted as parameter dependence of solutions of the Cauchy-Riemann operator.

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Parameter dependence of solutions of the Cauchy–Riemann equation on weighted spaces of smooth functions

Kruse

2020

RACSAM

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Surjectivity of the ̄∂-operator between weighted spaces of smooth vector-valued functions

Kruse

2021

Complex Variables and Elliptic Equations

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Solvability of the inhomogeneous Cauchy–Riemann equation in projective weighted spaces

Cited by 2 publications

References 24 publications

Parameter dependence of solutions of the Cauchy–Riemann equation on weighted spaces of smooth functions

Parameter dependence of solutions of the Cauchy–Riemann equation on weighted spaces of smooth functions

Surjectivity of the ̄∂-operator between weighted spaces of smooth vector-valued functions

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